Dept. of Mathematics, Ramakrishna Mission Vivekananda Educational and Research Institute (RKMVERI) has organised an colloquia on “Volumes of Hermitian Quadrics in Complex Projective Space” by Graduate Assistant, Department of Mathematics, Central Michigan University, USA on 12 August 2026.
Title: Volumes of Hermitian Quadrics in Complex Projective Space
Abstract:
The computation of volumes of domains in complex projective space is an interesting problem in Kähler geometry. In this talk, we consider domains bounded by Hermitian quadrics determined by Hermitian matrices. We derive a closed-form formula for the volume of such domains with respect to the Fubini–Study metric. The resulting volume depends only on the eigenvalues of the defining matrix and is symmetric in its positive and negative eigenvalues. Furthermore, the volume admits an explicit expression as a rational function of these eigenvalues. The proof combines geometric methods with identities involving Schur polynomials, highlighting the interplay between complex projective geometry, symmetric functions, and spectral properties of Hermitian matrices. The necessary geometric and algebraic background will be briefly reviewed.
| Faculty/Staff Name | Details |
|---|---|
| Stephan Baier | Mathematics – Belur Campus |
| S Ilangovan (Primary Coordinator) | Mathematics – Belur Campus |
| RKMVERI Faculty & Staff | 8 |
| RKMVERI Students | 30 |